Subtract the following rational expressions. $\dfrac{3-10z}{10z^2-3}-\dfrac{12z+5}{10z^2-3}=$
We want to subtract two rational expressions whose denominators are equal. We can do this by subtracting the numerators and keeping the denominator the same. [Does this fit with how we subtract rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{3-10z}{10z^2-3}-\dfrac{12z+5}{10z^2-3} \\\\ &=\dfrac{(3-10z)-(12z+5)}{10z^2-3} \\\\ &=\dfrac{3-10z-12z-5}{10z^2-3} \\\\ &=\dfrac{-22z-2}{10z^2-3} \end{aligned}$ In conclusion, $\dfrac{3-10z}{10z^2-3}-\dfrac{12z+5}{10z^2-3}=\dfrac{-22z-2}{10z^2-3}$